docs: def Beattie_Whalley(x, mul, mug, rhol, rhog):
      r'''Calculates a suggested definition for liquid-gas two-phase flow 
      viscosity in internal pipe flow according to the form in [1]_ and shown
      in [2]_ and [3]_.
          
      .. math::
          \mu_m = \mu_l(1-\alpha_m)(1 + 2.5\alpha_m) + \mu_g\alpha_m
          
      .. math::
          \alpha_m = \frac{1}{1 + \left(\frac{1-x}{x}\right)\frac{\rho_g}{\rho_l}}
          \text{(homogeneous model)}
  
      Parameters
      ----------
      x : float
          Quality of the gas-liquid flow, [-]
      mul : float
          Viscosity of liquid, [Pa*s]
      mug : float
          Viscosity of gas, [Pa*s]
      rhol : float
          Density of the liquid [kg/m^3]
      rhog : float
          Density of the gas [kg/m^3]
  
      Returns
      -------
      mu_lg : float
          Liquid-gas viscosity (**a suggested definition, potentially useful
          for empirical work only!**) [Pa*s]
  
      Notes
      -----
      This model converges to the liquid or gas viscosity as the quality
      approaches either limits.
          
      Examples
      --------
      >>> Beattie_Whalley(x=0.4, mul=1E-3, mug=1E-5, rhol=850, rhog=1.2)
      1.7363806909512365e-05
  
      References
      ----------
      .. [1] Beattie, D. R. H., and P. B. Whalley. "A Simple Two-Phase Frictional
         Pressure Drop Calculation Method." International Journal of Multiphase 
         Flow 8, no. 1 (February 1, 1982): 83-87. 
         doi:10.1016/0301-9322(82)90009-X. 
      .. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for 
         Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33,
         no. 1 (October 1, 2008): 106-13. 
      .. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and
         Predictive Methods for Pressure Drop in Adiabatic, Condensing and
         Boiling Mini/Micro-Channel Flows." International Journal of Heat and
         Mass Transfer 77 (October 2014): 74-97.
         doi:10.1016/j.ijheatmasstransfer.2014.04.035.
      '''
      alpha = homogeneous(x, rhol, rhog)
      return mul*(1. - alpha)*(1. + 2.5*alpha) + mug*alpha